U.S. patent number 8,390,371 [Application Number 12/848,006] was granted by the patent office on 2013-03-05 for tunable transconductance-capacitance filter with coefficients independent of variations in process corner, temperature, and input supply voltage.
This patent grant is currently assigned to TiaLinx, Inc.. The grantee listed for this patent is Mohammad Ardehali. Invention is credited to Mohammad Ardehali.
United States Patent |
8,390,371 |
Ardehali |
March 5, 2013 |
Tunable transconductance-capacitance filter with coefficients
independent of variations in process corner, temperature, and input
supply voltage
Abstract
A transconductance-capacitance (G.sub.m-C) filter of arbitrary
order is provided that is biased by a bias circuit such that the
G.sub.m-C filter is robust to variations in process corner and
temperature as well as input supply noise. The bias circuit
includes a biased transistor that has a width-to-length ratio that
is a factor X times larger than a corresponding transistor in the
G.sub.m-C filter. The biased transistor couples to ground through a
switched capacitor circuit.
Inventors: |
Ardehali; Mohammad (Newport
Beach, CA) |
Applicant: |
Name |
City |
State |
Country |
Type |
Ardehali; Mohammad |
Newport Beach |
CA |
US |
|
|
Assignee: |
TiaLinx, Inc. (Newport Beach,
CA)
|
Family
ID: |
45526114 |
Appl.
No.: |
12/848,006 |
Filed: |
July 30, 2010 |
Prior Publication Data
|
|
|
|
Document
Identifier |
Publication Date |
|
US 20120025899 A1 |
Feb 2, 2012 |
|
Current U.S.
Class: |
327/554; 330/261;
327/552 |
Current CPC
Class: |
H03H
11/0433 (20130101); H03H 11/0472 (20130101); H03H
2210/021 (20130101) |
Current International
Class: |
H04B
1/10 (20060101) |
Field of
Search: |
;327/552-554 |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: O'Neill; Patrick
Claims
I claim:
1. A transconductance-capacitance (G.sub.m-C) filter, comprising: a
plurality of operational transconductance amplifiers (OTAs),
wherein each OTA includes a differential pair of transistors
providing a tail current to a third transistor having a
transconductance g.sub.m, and a bias circuit for biasing a gate of
a given one of the third transistors with a control voltage, the
bias circuit including a switched capacitor circuit such that a
transfer function for the G.sub.m-C filter is proportional to a
ratio of capacitances and is independent of process corner
variations, wherein the bias circuit includes a fourth transistor
matched to the given third transistor and a fifth transistor that
has a width-to-length ratio that is a factor X times larger than a
width-to-length ratio for the fourth transistor, and wherein the
switched capacitor circuit is coupled between a source for the
fifth transistor and ground.
2. The G.sub.m-C filter of claim 1, wherein the transfer function
for the G.sub.m-C filter is independent of temperature
variations.
3. The G.sub.m-C filter of claim 1, wherein the transfer function
for the G.sub.m-C filter is independent of power supply noise.
4. The G.sub.m-C filter of claim 1, wherein the bias circuit
further comprises a first PMOS transistor, wherein the fourth
transistor is a diode-connected NMOS transistor coupled between a
drain of the first PMOS transistor and ground, and wherein the
fourth transistor has a gate coupled to a gate of the fifth
transistor.
5. The G.sub.m-C filter of claim 4, wherein the bias circuit
further comprises a second diode-connected PMOS transistor, wherein
the a drain of the second PMOS transistor couples to a drain of the
fifth transistor and wherein a gate of the first PMOS transistor
couples to a gate of the second PMOS transistor.
6. The G.sub.m-C filter of claim 5, wherein a source for each of
the first and second PMOS transistors couples to a power supply
voltage node.
7. The G.sub.m-C filter of claim 6, wherein the control voltage
equals a gate voltage for the fourth transistor.
8. A transconductance-capacitance (G.sub.m-C) filter, comprising a
plurality of operational transconductance amplifiers (OTAs),
wherein a first one of the OTAs has a first transconductance and
the remaining ones of the OTAs have transconductances that are
proportional to the first transconductance, and a bias circuit for
biasing the first transconductance to a desired value responsive to
a clock frequency, the bias circuit including a switched capacitor
circuit generating a resistance inversely proportional to the clock
frequency, wherein the desired transconductance value is
proportional to the clock frequency, wherein the first OTA includes
a first transistor having a gate driven by a bias voltage produced
by the bias circuit, and wherein the bias circuit includes a second
transistor having a width-to-length ratio that is a factor X times
larger than a width-to-length ratio of the first transistor, and
wherein the desired transconductance value is proportional to a
factor of (1-1/X.sup.1/2).
9. The G.sub.m-C filter of claim 8, wherein the G.sub.m-C filter is
a biquad filter.
Description
TECHNICAL FIELD
The present invention relates generally to filters, and more
particularly to tunable transconductance-capacitance (G.sub.m-C)
filters.
BACKGROUND
Transconductance-capacitance (G.sub.m-C) filters offer attractive
performance characteristics. Thus, the use of G.sub.m-C filters is
widespread and pervasive in radio communications and signal
processing. Analog G.sub.m-C filters are constructed using
operational transconductance amplifiers (OTAs). OTAs operate to
translate a voltage input signal into a current output signal. An
example balanced (differential output) OTA is shown in FIG. 1a. The
transconductance G.sub.m for the OTA determines the I.sup.+ and
I.sup.- currents based upon the input voltages V.sup.+ and V.sup.-
according to the following equations:
I.sup.+=G.sub.m(V.sup.+-V.sup.-) I.sup.-=G.sub.m(V.sup.--V.sup.+)
Various approaches are known to construct OTAs such as using
cascodes or differential architectures. A simple analog
transconductance-capacitance (G.sub.m-C) filter may be constructed
using a single-ended OTA as shown in FIG. 1b. If a time constant
.tau. is defined as C.sub.1/G.sub.m, then it can be shown that
V.sub.in for this filter equals V.sub.out+.tau.d(V.sub.out(t)/dt.
The cutoff frequency for the resulting G.sub.m-C filter will thus
rely on both G.sub.m and C.sub.1. But process corner variations
will typically be in the range of 20% for a desired capacitance
whereas a desired transconductance will have process corner
variations in the range of 10%. It follows that the resulting time
constant .tau. for such a filter will be accurate to just 30%
across all the process corner variations. Moreover,
transconductance values will vary significantly with temperature
and the supply voltage level. In addition, input noise will
introduce variations in the filter coefficients. Accordingly, it is
conventional to provide some sort of tuning circuitry on G.sub.m-C
filters. In this fashion, a tunable G.sub.m-C filter has its time
constant set to some desired value with some isolation from
variations in the power supply voltage, process corner, and
temperature.
Although such independence is desirable, conventional tunable
G.sub.m-C filters are still sensitive to power supply variations
and suffer from non-idealities. Accordingly, there is a need in the
art for improved tunable G.sub.m-C filters that are more robust to
variations in process corner, power supply, and temperature.
SUMMARY
In accordance with one aspect of the invention, a
transconductance-capacitance (G.sub.m-C) filter is provided that
includes: a plurality of operational transconductance amplifiers
(OTAs), wherein a first one of the OTAs has a first
transconductance and the remaining ones of the OTAs have
transconductances that are proportional to the first
transconductance, and a bias circuit for biasing the first
transconductance to a desired value responsive to a clock
frequency, the bias circuit including a switched capacitor circuit
generating a resistance inversely proportional to the clock
frequency, wherein the desired transconductance value is
proportional to the clock frequency.
In accordance with another aspect of the invention, a
transconductance-capacitance (G.sub.m-C) filter is provided that
includes: a plurality of operational transconductance amplifiers
(OTAs), wherein each OTA includes a differential pair of
transistors providing a tail current to a third transistor having a
transconductance g.sub.m, and a bias circuit for biasing a gate of
a given one of the third transistors with a control voltage, the
bias circuit including a switched capacitor circuit such that a
transfer function for the G.sub.m-C filter is proportional to a
ratio of capacitances and is independent of process corner
variations.
In accordance with yet another aspect of the invention, a bias
circuit to bias the transconductance g.sub.m of a first transistor
within a G.sub.m-C filter is provided that includes: a second
transistor having a width-to-length ratio that is a factor X larger
than a width-to-length ratio of the first transistor, the second
transistor coupling to ground through a switched capacitor circuit
such that g.sub.m is proportional to (1-1/X.sup.1/2).
The scope of the invention is defined by the claims, which are
incorporated into this section by reference. A more complete
understanding of embodiments of the present invention will be
afforded to those skilled in the art, as well as a realization of
additional advantages thereof, by a consideration of the following
detailed description of one or more embodiments. Reference will be
made to the appended sheets of drawings that will first be
described briefly.
BRIEF DESCRIPTION OF DRAWINGS
FIG. 1a is a schematic diagram of an operational transconductance
amplifier (OTA).
FIG. 1b is a schematic diagram of a conventional
transconductance-capacitance (G.sub.m-C) filter.
FIG. 2 is a schematic diagram of a biquad G.sub.m-C filter tuned
using a switched-capacitor bias circuit.
FIG. 3 is a circuit diagram of a differential amplifier within an
OTA in the filter of FIG. 2.
FIG. 4a is a circuit diagram illustrating the equivalence of a
switched capacitor circuit to a resistor.
FIG. 4b is a circuit diagram of a switched capacitor circuit
adapted for greater robustness to parasitic effects.
FIG. 5 is a circuit diagram for a bias circuit to provide the
control voltage applied in the circuit of FIG. 3.
Embodiments of the present invention and their advantages are best
understood by referring to the detailed description that follows.
It should be appreciated that like reference numerals are used to
identify like elements illustrated in one or more of the
figures.
DETAILED DESCRIPTION
Reference will now be made in detail to one or more embodiments of
the invention. While the invention will be described with respect
to these embodiments, it should be understood that the invention is
not limited to any particular embodiment. On the contrary, the
invention includes alternatives, modifications, and equivalents as
may come within the spirit and scope of the appended claims.
Furthermore, in the following description, numerous specific
details are set forth to provide a thorough understanding of the
invention. The invention may be practiced without some or all of
these specific details. In other instances, well-known structures
and principles of operation have not been described in detail to
avoid obscuring the invention.
To provide a tunable G.sub.m-C filter that self-compensates with
regard to process corner variations, power supply variations, and
temperature variations, a switched capacitor circuit is used to
tune the transconductance G.sub.m of one of more of the OTAs
included within the G.sub.m-C filter. In that regard, a biquad
second order G.sub.m-C filter such as filter 100 shown in FIG. 2
includes five different OTAs, each having their own independent
transconductance (denoted as g.sub.m1 through g.sub.m5). In
addition, filter 100 includes 3 classes of capacitors (having
corresponding capacitances C.sub.1 through C.sub.3). The transfer
function H(s) for filter 100 thus depends on the various
transconductances and capacitances as given by the following
equation:
.function..function..function..times..times..times..times..times..times..-
times..function..function..times..times..times..times..times..times..times-
..function. ##EQU00001## This relatively complex behavior can be
simplified as follows. Although transconductances have large
variations in their absolute values, relative transconductance
values can be set quite accurately by the ratio of the OTA
transistor widths (provided the same channel lengths are used for
all devices). Thus, an arbitrary OTA such as OTA 105 having a
transconductance g.sub.m1 may be used to define the
transconductance of the remaining OTAs. For example, the
transconductance g.sub.m2 for OTA 110 may be defined as
K.sub.m2g.sub.m1, the transconductance g.sub.m3 for OTA 115 may be
defined as K.sub.m3g.sub.m1, and so on. In general, the ith
transconductance can be expressed in terms of the first OTA as
G.sub.mi=K.sub.miG.sub.mi (2) Similarly, the sum of the
capacitances C.sub.3 and C.sub.2 can be defined in terms of C1
using a constant K as C.sub.3+C.sub.2=KC.sub.1 (3) Using equations
(2) and (3), equation (1) can be simplified as follows
.function..function..function..times..times..times..times..times..times..-
times..times..times..times..times..times..times..function..times..times..t-
imes..times..times..times..times..times..times..times..times..times..times-
. ##EQU00002## From equation (4), it can be seen that if just the
ratio of Gm1/C1 is tuned to be self-compensating with regard to
variations in power supply, process corner, and temperature, then
the remaining transconductance/capacitance ratios need no tuning
since these ratios can be conventionally manufactured to an
accuracy of approximately one percent.
Although the above simplification was described with regard to the
biquad filter 100 of FIG. 1, it can be shown that any order (nth
order) of G.sub.m-C filters can be tuned in this fashion. In other
words, a single one of the OTAs may be self-compensated as
discussed further herein yet the entire G.sub.m-C filter will be
self-compensated. This self-compensation may be better understood
with reference to the transistor differential pair within each OTA.
An example differential pair of matched transistors M1 and M2 is
shown in FIG. 3. The tail current from transistor M1 and M3 is
biased by a control voltage V.sub.cntl driving the gate of a
transistor M3. Matched transistors M1 and M2 each have a
transconductance of G.sub.m whereas M3 is sized to have a
transconductance of AG.sub.m.
The following discussion will show how to generate the bias voltage
V.sub.cntl such that the ratio of G.sub.m/C.sub.L for the OTA is
self-compensating. This self compensation will rely on the use of a
switched capacitor circuit to produce a desired resistance. As
known from Ohm's law, a voltage potential V.sub.A-V.sub.B applied
across a resistor of resistance R will produce a current I equaling
(V.sub.A-V.sub.B)/R. However, as seen in FIG. 4a, the same amount
of charge can be moved between these voltage potentials using a
switched capacitor circuit 400 that couples voltage V.sub.A to a
capacitor having a capacitance C.sub.ck through a switch S.sub.1.
Similarly, the capacitor couples to voltage V.sub.B through a
switch S.sub.2. If switched S.sub.1 is driven on and off by a clock
of frequency f.sub.ck while switch S.sub.2 is driven by the
complement of this clock, it can be shown that a current I flowing
through the capacitor will equal f.sub.ckC.sub.ck(V.sub.A-V.sub.B).
Thus, the switched capacitor circuit functions as a resistor having
a resistance R.sub.m of R.sub.m=1/f.sub.ckC.sub.ck (5) The
equivalence of a switched capacitor circuit to provide a desired
resistance is made more precise by using the additional switches
S.sub.3 and S.sub.4 as shown in FIG. 4b for a switched capacitor
circuit 405 in that the additional switches make the circuit
parasitic insensitive. S.sub.1 and S.sub.4 are driven by the clock
whereas S.sub.2 and S.sub.3 are driven by the complement of the
clock.
The incorporation of a switched capacitor circuit into a bias
circuit 500 as shown in FIG. 5 for the generation of the control
voltage V.sub.cntl will now be discussed. A pair of PMOS
transistors P.sub.1 and P.sub.2 form a current mirror. Thus, if
P.sub.1 and P.sub.2 are matched (same width W and length L and thus
the same W/L ratio), they will each source the same current I.
Thus, a current I flows through an NMOS transistor M.sub.4 and an
NMOS transistor M.sub.5. M4 is diode connected between the drain of
a PMOS transistor P.sub.1 and ground so as to be in saturation
mode. Transistor M.sub.4 is matched to M.sub.3 of FIG. 3. The gate
of M.sub.4 is tied to the gate of transistor M.sub.5, where M.sub.5
is larger than M.sub.4. If M.sub.5 has the same length L as does
M.sub.4, then the width of M.sub.5 is a factor X times larger than
a width W for M.sub.4. The sources of both P.sub.1 and P.sub.2 are
driven by a power supply voltage node V.sub.CC. The source of
M.sub.5 couples to ground through a switched capacitor circuit 505
that functions to provide a resistance of R.sub.m. It can be shown
that the transconductance g.sub.m4 for M.sub.4 can be expressed as
g.sub.m4=2/R.sub.m(1-1/Sqrt(X)) (6) Substitution of equation (5)
into equation (6) allows the transconductance to be expressed as
g.sub.m4=2(1-1/Sqrt(X))f.sub.ckC.sub.ck (7) It will be appreciated
that the switched capacitor circuit 505 may be made more robust as
discussed with regard to FIG. 4b. Examination of equation (7) shows
that the transconductance dependence on the width X is such that by
making X sufficiently large, the necessary clock frequency for
driving the switched capacitor circuit is reduced. This is a
substantial advantage over other techniques used to make G.sub.m-C
filters more robust to variations in power supply voltage (input
noise), process corners, and temperature.
Referring back to FIG. 3, one can see that if the transconductance
of M.sub.3 is controlled by the control voltage V.sub.cntl
generated as discussed with regard to FIG. 5, the ratio of
G.sub.m/C.sub.L for the OTA/capacitor combination including such a
differential pair can be expressed as
G.sub.m/C.sub.L=2A(1-1/Sqrt(X))f.sub.ckC.sub.ck/C.sub.L (8)
Referring again to FIG. 2, suppose that the OTAs were all matched
in the sense of having matched differential pairs of transistors as
discussed with regard to FIG. 3. It has already been shown with
regard to equation (4) that if just one of the transconductances is
tuned, then the overall G.sub.m-C for the filter is established. As
seen by equation (8), the filter coefficients will depend only on
the ratio of device parameters and capacitances. This is quite
advantageous as the resulting filter coefficients will be
independent of process and temperature variations as well as power
supply noise. For example, a fast process corner will affect
C.sub.ck equally as it does affect C.sub.L. Thus, the ratio of
capacitances cancels out process corner variations. The same
argument applies to temperature and power supply noise. Moreover,
although this self compensation of a G.sub.m-C filter has been
discussed with regard to the biquad filter 100 of FIG. 2, the same
self-compensation can be applied to any nth order G.sub.m-C
filter.
It will be obvious to those skilled in the art that various changes
and modifications may be made without departing from this invention
in its broader aspects. The appended claims encompass all such
changes and modifications as fall within the true spirit and scope
of this invention.
* * * * *